Undepleted Pump Regime Research Articles

Homogenization and Scattering Analysis of Second-Harmonic Generation in Nonlinear Metasurfaces

We propose an extensive discussion on the homogenization and scattering analysis of second-order nonlinear metasurfaces. Our developments are based on the generalized sheet transition conditions (GSTCs) which are used to model the electromagnetic responses of nonlinear metasurfaces. The GSTCs are solved both in the frequency domain, assuming an undepleted pump regime, and in the time-domain, assuming dispersionless material properties but a possible depleted pump regime. Based on these two modeling approaches, we derive the general second-harmonic reflectionless and transmissionless conditions as well as the conditions of asymmetric reflection and transmission. We also discuss and clarify the concept of nonreciprocal scattering pertaining to nonlinear metasurfaces.

Extended parametric gain range in photonic crystal fibers with strongly frequency-dependent field distributions.

The parametric gain range of a degenerate four-wave mixing process is determined in the undepleted pump regime. The gain range is considered with and without taking the mode field distributions of the four-wave mixing components into account. It is found that the mode field distributions have to be included to evaluate the parametric gain correctly in dispersion-tailored speciality fibers and that mode profile engineering can provide a way to increase the parametric gain range.

Peculiarities of the single and repetitive pulse threshold pump power for stimulated Brillouin scattering in long optical fibres

It is shown that in the undepleted pulsed pump regime of stimulated Brillouin scattering (SBS) the duration of a Stokes pulse in long optical fibres increases by the doubled time of flight for a pump pulse through a fibre. A consequence of this is up to three times difference between the SBS threshold power in a single pump pulse regime when the instant power or energy of the scattered radiation is measured. A distinguishing peculiarity of a repetitive pump pulse regime is a stepwise reduction of the threshold power with the decrease of an interpulse interval when the interval equals the doubled time of flight for a pump pulse through a fibre.

Numerical modelling of the pump-to-signal relative intensity noise transfer in two-pump fibre optical parametric amplifiers

An accurate numerical model to investigate the pump-to-signal relative intensity noise (RIN) transfer in two-pump fibre optical parametric amplifiers (2-P FOPAs) for low modulation frequencies is presented. Compared to other models in the field, this model takes into account the fibre loss, pump depletion as well as the gain saturation. As a result, the model allows to include a wide range of practical circumstances, both in and beyond the undepleted pump regime, related to different applications of FOPAs. In the small-signal or undepleted pump regime, the model predicts the ripples of the RIN spectrum very well and yields better results than those of other models. It is shown that beyond the small-signal regime, pump power variations do not remain unchanged over the length of the amplifier and for high signal powers, when the FOPA saturates, minimum pump-to-signal RIN transfer occurs. The results of the model are also compared with the available experimental data in the field and a very good agreement can be seen.

Design and optimization of phase regenerator with photonic crystal fiber

Amplification and simultaneous phase regeneration of differential phase-shift keying （DPSK） signals is demonstrated using a phase regenerator. Phase regeneration is achieved in a Sagnac fiber interferometer comprised of photonic crystal fiber operating in an un-depleted pump regime. The formula of signal after phase regenerator is derived. For different incident power of signal, the relations between signal-pump phase difference and signal gain are discussed, as well as the influence of fiber length on signal output intensity. The optimum parameters of the phase regenerator are given. The distributions of phase and intensities for both the non-regenerated and regenerated signals are simulated. Simulations show that nearly ideal regeneration can be achieved for the DPSK signals.

Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers

The polarization properties of stimulated Brillouin scattering (SBS) amplification or attenuation in standard single-mode fibers are examined through vectorial analysis, simulation and experiment. Vector propagation equations for the signal wave, incorporating SBS and birefringence, are derived and analyzed in both the Jones and Stokes spaces. The analysis shows that in the undepleted pump regime, the fiber may be regarded as a polarization-dependent gain (or loss) medium, having two orthogonal input SOPs, and corresponding two orthogonal output SOPs, for the signal, which, respectively, provide the signal with maximum and minimum SBS amplification (or attenuation). Under high Brillouin gain conditions and excluding zero-probability cases, the output SOP of arbitrarily polarized input signals, would tend to converge towards that of maximum SBS gain. In the case of high SBS attenuation the output SOP of an arbitrarily polarized signal would approach the output SOP corresponding to minimum attenuation. It is found that for a wide range of practical pump powers ( < or = 100mW) and for sufficiently long fibers with typical SBS and birefringence parameters, the signal aligned for maximum SBS interaction will enter/emerge from the fiber with its electric field closely tracing the same ellipse in space as that of the pump at the corresponding side of the fiber, albeit with the opposite sense of rotation. The analytic predictions are experimentally demonstrated for both Stokes (amplification) and anti-Stokes (attenuation) signals.

Designer femtosecond pulse shaping using grating-engineered quasi-phase-matching in lithium niobate

The generation of tailored femtosecond pulses with fully engineered intensity and phase profiles is demonstrated using second-harmonic generation of an Er:fiber laser in an aperiodically poled lithium niobate crystal in the undepleted pump regime. Second-harmonic pulse shapes, including Gaussian, stepped, square, and multiple pulses have been characterized using cross-correlation frequency-resolved optical gating and have been shown to agree well with theory.

Exact analytical treatment of noise initiation of SBS in the presence of loss

An exact analytical expression for the Stokes power generated by stimulated Brillouin scattering in a lossy medium is derived for the first time. The approach is based on a distributed, fluctuating source model in the undepleted pump regime, previously only rigorously applied to lossless media. A comparison with known approximations is performed.

Demonstration of phase-regeneration of DPSK signals based on phase-sensitive amplification

Amplification and simultaneous phase regeneration of DPSK signals is demonstrated using a phase-sensitive amplifier. Phase-sensitive gain is achieved in a Sagnac fiber interferometer comprised of nonpolarization maintaining, highly nonlinear fiber operating in the un-depleted pump regime. Both the pump and signal are RZ-DPSK pulse trains. The amplifier is capable of producing greater than 13 dB of phase-sensitive gain for an average pumping power of 100 mW, and easily reduces the BER of the regenerated DPSK signal by two orders of magnitude compared to the un-regenerated signal, corresponding to a negative power penalty of 2 dB. Careful optimization of the regenerator reveals much stronger BER Improvement.

All-optical regeneration of differential phase-shift keying signals based on phase-sensitive amplification

All-optical regeneration of differential phase-shift keying signals based on phase-sensitive amplification is described. Nearly ideal phase regeneration can be achieved in the undepleted-pump regime, and simultaneous amplitude and phase regeneration can be realized in the depleted-pump regime.

Exact analytic expressions for electromagnetic propagation and optical nonlinear generation in finite one-dimensional periodic multilayers

The translation matrix formalism has been used to find an exact analytic solution for linear light propagation in a finite one-dimensional periodic stratified structure. This modal approach allows us to derive a closed formula for the electric field in every point of the structure, by simply imposing a convenient form for the boundary conditions. We show how to apply this result to second-harmonic generation in the undepleted pump regime.

Quadratic Interactions in Finite, One-Dimensional, Photonic Band Gap Structures with Deep Gratings: beyond the Undepleted Pump Regime

We theoretically study quadratic interactions in finite, one-dimensional, photonic band gap structures with deep gratings, under strong pumping and global phase matching conditions. For second harmonic generation, we findthat above a certain input intensity a dynamics reminiscent of a competitive, multi-wave mixing process takes hold: the pump field is mostly reflected, revealing a novel type of optical limiting behavior, while forward and backward generation is generally balanced. We also study the case of parametric down-conversion, where an intense second harmonic signal is injected in order to control a much weaker fundamental beam. Our results reveal the onset of a new process that has no counterpart in bulk materials: both transmission and reflection display an unexpected, unusual, resonance-like effect as functions of input second harmonic power.

Generalized coupled-mode theory for χ^(2) interactions in finite multilayered structures

Using a first-order multiple-scale expansion approach, we derive a set of coupled-mode equations that describe both forward and backward second-harmonic generation and amplification processes in nonlinear, one-dimensional, multilayered structures of finite length. The theory is valid for index modulation of arbitrary depth and profile. We derive analytical solutions in the undepleted pump regime under different pumping circumstances. The model shows excellent agreement with the numerical integration of Maxwell’s equations.

Phase independent nonlinear amplification regime in one-dimensional photonic bandgaps

A simple way to study parametric amplification in finite layered structures with an optical nonlinear quadratic response is theoretically analysed. We show that it is possible to write equations that are formally equivalent to those of a bulk medium and that we are able to analyse the effective behaviour of the structure. Then we give the solutions of these effective equations in the undepleted pump regime and use semiconducting materials to theoretically study a structure that gives a good amplification of the signal.

Pump-power-dependent gain for small-signal parametric amplification in birefringent fibres

The nonlinear dependence of the parametric gain for small-signal amplification is experimentally studied in a normally dispersive highly birefringent single-mode fibre. As a result of the pump-induced nonlinear phase shift, the signal gain curve versus the pump power is bell shaped in the undepleted-pump regime with maximum gain attained away from perfect phase-matching. This dynamics is quite different from the quasi-exponential gain measured for spontaneous parametric emission growing from noise. Moreover, the experimental gain curves are more accurately predicted by modulation instability computations rather than four-wave mixing theory because of the influence of the non-phase-matched waves.

Type-II frequency doubling at λ = 130 µm and λ = 253 µm in flux-grown potassium titanyl phosphate

Continuous-wave type-II (oeo) second-harmonic-generation (SHG) characterization of the linear and nonlinear properties of KTiOPO4 in the mid-IR range with a InGaAsP diode laser at λ = 1.30 μm and a tunable KCl:Li color-center laser at λ = 2.53 μm are reported. With accurate phase-matching-angle measurements we have tested the accuracy of the numerous published Sellmeier data. We also discuss a birefringence-assisted noncollinear phase-matching technique as an efficient means to increase the coherence length of type-II walk-off-limited SHG. Through measurements of the angular and wavelength acceptance bandwidths and experimental analysis of the far-field second-harmonic transverse pattern, we provide an experimental test of the relevancy of the modified Boyd–Kleinman theory of the walk-off-limited type-II parametric interaction. Measured values of the d24 nonlinear susceptibility at λ = 0.65 μm (d24 = 2.45 pm/V) and λ = 1.265 μm (d24 = 2.30 pm/V) with an accuracy of 8.5% have been deduced from our conversion-efficiency measurements performed in the undepleted cw pump regime. The extrapolated value at λ = 0.532 μm (d24 = 2.58 pm/V) is found to be 30% smaller than those reported thus far from phase-matched pulsed measurements.

Two-wave mixing of time-varying non-plane-wave optical fields in photorefractive materials

A theoretical analysis is presented of two-wave mixing in photorefractive materials in which the complex amplitude of a weak signal beam has slowly varying but otherwise arbitrary spatial dependence and arbitrary time variation. The set of coupled partial differential equations that couple the dynamics of the optical fields to the photorefractive medium is solved analytically to give the complex amplitude of the transmitted signal in the undepleted pump regime. The results are compared with known results for the transient two-wave mixing of plane waves.

Undepleted pump regime of Hill grating formation in optical fibers

A bleaching model describing the dynamics of Hill grating formation in optical fibers, [K.O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978)], is analytically solved in an undepleted pump approximation. This regime provides quantitative predictions about grating dynamics in the early stages of grating growth. A series of experiments in which heating effects and surface reflections from the input end of the fiber have been eliminated show quantitative agreement with the theory to 2%.

Quasi-steady-state regime in transient stimulated Raman scattering.

A method is developed for studying transient stimulated Raman scattering in the quasi-steady-state regime when the input pump field consists of a repetitive periodic sequence of pulses. The method is most attractive for cases where the single-pulse duration is substantially shorter than the repetition time scale, making a straightforward numerical simulation very costly, time consuming, and potentially intractable. The method is applicable to any periodic electric field envelope including that generated by a finite number of longitudinal modes with arbitrary phase. A second numerically efficient method is developed for treating the buildup of the entire pulse train. In addition, an analytic solution is found in the undepleted-pump regime which illuminates the underlying physics of the process.